Is there a clear numerical definition of the word MINIMUM???

[Lil' Lavery]

As just mentioned, unless given further information, the minimum is -∞. If you are given a certain domain/range that may adjust it, as could the function itself (if it never reaches -∞ for whatever reason).
In the scalar world, it's zero (unless the function never reaches 0).

[GaryVoshol]

When you have a statement such as, "There is no minimum age", that does not mean that the minimum age defined is some abitrarily small number. Rather, it is just what it says - it is not defined. Null, which is different than zero.

My algebra teacher always got mad (jokingly) at Ernie Harwell, the legendary Tigers announcer. He had a shtick line that went, "And at the end of 3, we have no score." My teacher said, yes there was a score - it was 0 to 0! He used this as an example of the difference between zero and null.